Let $(k,\operatorname{ord})$ be a valued local (or even just henselian field), $\tilde{k}$ its algebraic closure. Let $\alpha\in \tilde{k}$. Define the diameter of $\alpha$ as
$$\Delta_k(\alpha) = \Delta(\alpha) = \min \{\operatorname{ord}(\alpha'-\alpha)\mid \alpha'\in \tilde{k}, k\text{-conjugate to } \alpha\}.$$
To gain a better understanding, I would like to explicitly compute $\Delta(\alpha)$ for some $\alpha\in \overline{\mathbb{Q}}_p$ (perhaps $3+i2\in\overline{\mathbb{Q}}_3$). How would I do this?